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Optimization · Zero-order and Black-box Optimization

Jaewon Chu, Jinyoung Park, Seunghun Lee, Hyunwoo Kim

Latent Bayesian optimization (LBO) approaches have successfully adopted Bayesian optimization over a continuous latent space by employing an encoder-decoder architecture to address the challenge of optimization in a high dimensional or discrete input space. LBO learns a surrogate model to approximate the black-box objective function in the latent space. However, we observed that most LBO methods suffer from the `misalignment problem', which is induced by the reconstruction error of the encoder-decoder architecture. It hinders learning an accurate surrogate model and generating high-quality solutions. In addition, several trust region-based LBO methods select the anchor, the center of the trust region, based solely on the objective function value without considering the trust region's potential to enhance the optimization process. To address these issues, we propose $\textbf{Inv}$ersion-based Latent $\textbf{B}$ayesian $\textbf{O}$ptimization (InvBO), a plug-and-play module for LBO. InvBO consists of two components: an inversion method and a potential-aware trust region anchor selection. The inversion method searches the latent code that completely reconstructs the given target data. The potential-aware trust region anchor selection considers the potential capability of the trust region for better local optimization. Experimental results demonstrate the effectiveness of InvBO on nine real-world benchmarks, such as molecule design and arithmetic expression fitting tasks. Code is available at https://github.com/mlvlab/InvBO.

Optimization · Large Scale, Parallel and Distributed

XINNUO XU, Minyoung Kim, Royson Lee, Brais Martinez, Timothy Hospedales

Data point selection (DPS) is becoming a critical topic in deep learning due to the ease of acquiring uncurated training data compared to the difficulty of obtaining curated or processed data. Existing approaches to DPS are predominantly based on a bi-level optimisation (BLO) formulation, which is demanding in terms of memory and computation, and exhibits some theoretical defects regarding minibatches.Thus, we propose a novel Bayesian approach to DPS. We view the DPS problem as posterior inference in a novel Bayesian model where the posterior distributions of the instance-wise weights and the main neural network parameters are inferred under a reasonable prior and likelihood model.We employ stochastic gradient Langevin MCMC sampling to learn the main network and instance-wise weights jointly, ensuring convergence even with minibatches. Our update equation is comparable to the widely used SGD and much more efficient than existing BLO-based methods. Through controlled experiments in both the vision and language domains, we present the proof-of-concept. Additionally, we demonstrate that our method scales effectively to large language models and facilitates automated per-task optimization for instruction fine-tuning datasets.

Causality

Yu Xiang, Jie Qiao, Zefeng Liang, Zihuai Zeng, Ruichu Cai, Zhifeng Hao

Causal discovery from observational data, especially for count data, is essential across scientific and industrial contexts, such as biology, economics, and network operation maintenance. For this task, most approaches model count data using Bayesian networks or ordinal relations. However, they overlook the inherent branching structures that are frequently encountered, e.g., a browsing event might trigger an adding cart or purchasing event. This can be modeled by a binomial thinning operator (for branching) and an additive independent Poisson distribution (for noising), known as Poisson Branching Structure Causal Model (PB-SCM). There is a provably sound cumulant-based causal discovery method that allows the identification of the causal structure under a branching structure. However, we show that there still remains a gap in that there exist causal directions that are identifiable while the algorithm fails to identify them. In this work, we address this gap by exploring the identifiability of PB-SCM using the Probability Generating Function (PGF). By developing a compact and exact closed-form solution for the PGF of PB-SCM, we demonstrate that each component in this closed-form solution uniquely encodes a specific local structure, enabling the identification of the local structures by testing their corresponding component appearances in the PGF. Building on this, we propose a practical algorithm for learning causal skeletons and identifying causal directions of PB-SCM using PGF. The effectiveness of our method is demonstrated through experiments on both synthetic and real datasets.

Probabilistic Methods · Bayesian Models and Methods

Ioannis Zachos, Mark Girolami, Theodoros Damoulas

Agent-based models (ABMs) are proliferating as decision-making tools across policy areas in transportation, economics, and epidemiology. In these models, a central object of interest is the discrete origin-destination matrix which captures spatial interactions and agent trip counts between locations. Existing approaches resort to continuous approximations of this matrix and subsequent ad-hoc discretisations in order to perform ABM simulation and calibration. This impedes conditioning on partially observed summary statistics, fails to explore the multimodal matrix distribution over a discrete combinatorial support, and incurs discretisation errors. To address these challenges, we introduce a computationally efficient framework that scales linearly with the number of origin-destination pairs, operates directly on the discrete combinatorial space, and learns the agents' trip intensity through a neural differential equation that embeds spatial interactions. Our approach outperforms the prior art in terms of reconstruction error and ground truth matrix coverage, at a fraction of the computational cost. We demonstrate these benefits in two large-scale spatial mobility ABMs in Washington, DC and Cambridge, UK.

Probabilistic Methods · Tractable Models

Shivvrat Arya, Tahrima Rahman, Vibhav Gogate

We propose a novel neural networks based approach to efficiently answer arbitrary Most Probable Explanation (MPE) queries—a well-known NP-hard task—in large probabilistic models such as Bayesian and Markov networks, probabilistic circuits, and neural auto-regressive models. By arbitrary MPE queries, we mean that there is no predefined partition of variables into evidence and non-evidence variables. The key idea is to distill all MPE queries over a given probabilistic model into a neural network and then use the latter for answering queries, eliminating the need for time-consuming inference algorithms that operate directly on the probabilistic model. We improve upon this idea by incorporating inference-time optimization with self-supervised loss to iteratively improve the solutions and employ a teacher-student framework that provides a better initial network, which in turn, helps reduce the number of inference-time optimization steps. The teacher network utilizes a self-supervised loss function optimized for getting the exact MPE solution, while the student network learns from the teacher's near-optimal outputs through supervised loss. We demonstrate the efficacy and scalability of our approach on various datasets and a broad class of probabilistic models, showcasing its practical effectiveness.

Probabilistic Methods · Bayesian Models and Methods

Julius Vetter, Guy Moss, Cornelius Schröder, Richard Gao, Jakob H Macke

Scientific modeling applications often require estimating a distribution of parameters consistent with a dataset of observations - an inference task also known as source distribution estimation. This problem can be ill-posed, however, since many different source distributions might produce the same distribution of data-consistent simulations. To make a principled choice among many equally valid sources, we propose an approach which targets the maximum entropy distribution, i.e., prioritizes retaining as much uncertainty as possible. Our method is purely sample-based - leveraging the Sliced-Wasserstein distance to measure the discrepancy between the dataset and simulations - and thus suitable for simulators with intractable likelihoods. We benchmark our method on several tasks, and show that it can recover source distributions with substantially higher entropy than recent source estimation methods, without sacrificing the fidelity of the simulations. Finally, to demonstrate the utility of our approach, we infer source distributions for parameters of the Hodgkin-Huxley model from experimental datasets with hundreds of single-neuron measurements. In summary, we propose a principled method for inferring source distributions of scientific simulator parameters while retaining as much uncertainty as possible.

Reinforcement Learning · Batch Offline

Rui Yang, Jie Wang, Guoping Wu, Bin Li

Real-world offline datasets are often subject to data corruptions (such as noise or adversarial attacks) due to sensor failures or malicious attacks. Despite advances in robust offline reinforcement learning (RL), existing methods struggle to learn robust agents under high uncertainty caused by the diverse corrupted data (i.e., corrupted states, actions, rewards, and dynamics), leading to performance degradation in clean environments. To tackle this problem, we propose a novel robust variational Bayesian inference for offline RL (TRACER). It introduces Bayesian inference for the first time to capture the uncertainty via offline data for robustness against all types of data corruptions. Specifically, TRACER first models all corruptions as the uncertainty in the action-value function. Then, to capture such uncertainty, it uses all offline data as the observations to approximate the posterior distribution of the action-value function under a Bayesian inference framework. An appealing feature of TRACER is that it can distinguish corrupted data from clean data using an entropy-based uncertainty measure, since corrupted data often induces higher uncertainty and entropy. Based on the aforementioned measure, TRACER can regulate the loss associated with corrupted data to reduce its influence, thereby enhancing robustness and performance in clean environments. Experiments demonstrate that TRACER significantly outperforms several state-of-the-art approaches across both individual and simultaneous data corruptions.

Neuroscience, Cognitive Science

Top Piriyakulkij, Cassidy Langenfeld, Tuan Anh Le, Kevin Ellis

We give a model of how to infer natural language rules by doing experiments. Themodel integrates Large Language Models (LLMs) with Monte Carlo algorithms forprobabilistic inference, interleaving online belief updates with experiment designunder information-theoretic criteria. We conduct a human-model comparison on aZendo-style task, finding that a critical ingredient for modeling the human data is toassume that humans also consider fuzzy, probabilistic rules, in addition to assumingthat humans perform approximately-Bayesian belief updates. We also comparewith recent algorithms for using LLMs to generate and revise hypotheses, findingthat our online inference method yields higher accuracy at recovering the trueunderlying rule, and provides better support for designing optimal experiments.

Optimization · Optimization and Learning under Uncertainty

Theodore Brown, Alexandru Cioba, Ilija Bogunovic

Bayesian optimisation (BO) is a powerful framework for global optimisation of costly functions, using predictions from Gaussian process models (GPs). In this work, we apply BO to functions that exhibit invariance to a known group of transformations. We show that vanilla and constrained BO algorithms are inefficient when optimising such invariant objectives, and provide a method for incorporating group invariances into the kernel of the GP to produce invariance-aware algorithms that achieve significant improvements in sample efficiency. We derive a bound on the maximum information gain of these invariant kernels, and provide novel upper and lower bounds on the number of observations required for invariance-aware BO algorithms to achieve $\epsilon$-optimality. We demonstrate our method's improved performance on a range of synthetic invariant and quasi-invariant functions. We also apply our method in the case where only some of the invariance is incorporated into the kernel, and find that these kernels achieve similar gains in sample efficiency at significantly reduced computational cost. Finally, we use invariant BO to design a current drive system for a nuclear fusion reactor, finding a high-performance solution where non-invariant methods failed.

Probabilistic Methods · Monte Carlo and Sampling Methods

Zihui Wu, Yu Sun, Yifan Chen, Bingliang Zhang, Yisong Yue, Katherine Bouman

Diffusion models (DMs) have recently shown outstanding capabilities in modeling complex image distributions, making them expressive image priors for solving Bayesian inverse problems. However, most existing DM-based methods rely on approximations in the generative process to be generic to different inverse problems, leading to inaccurate sample distributions that deviate from the target posterior defined within the Bayesian framework. To harness the generative power of DMs while avoiding such approximations, we propose a Markov chain Monte Carlo algorithm that performs posterior sampling for general inverse problems by reducing it to sampling the posterior of a Gaussian denoising problem. Crucially, we leverage a general DM formulation as a unified interface that allows for rigorously solving the denoising problem with a range of state-of-the-art DMs. We demonstrate the effectiveness of the proposed method on six inverse problems (three linear and three nonlinear), including a real-world black hole imaging problem. Experimental results indicate that our proposed method offers more accurate reconstructions and posterior estimation compared to existing DM-based imaging inverse methods.

Probabilistic Methods · Bayesian Models and Methods

Fangyi Wang, Karthik Bharath, Oksana Chkrebtii, Sebastian Kurtek

The reliable recovery and uncertainty quantification of a fixed effect function $\mu$ in a functional mixed model, for modeling population- and object-level variability in noisily observed functional data, is a notoriously challenging task: variations along the $x$ and $y$ axes are confounded with additive measurement error, and cannot in general be disentangled. The question then as to what properties of $\mu$ may be reliably recovered becomes important. We demonstrate that it is possible to recover the size-and-shape of a square-integrable $\mu$ under a Bayesian functional mixed model. The size-and-shape of $\mu$ is a geometric property invariant to a family of space-time unitary transformations, viewed as rotations of the Hilbert space, that jointly transform the $x$ and $y$ axes. A random object-level unitary transformation then captures size-and-shape preserving deviations of $\mu$ from an individual function, while a random linear term and measurement error capture size-and-shape altering deviations. The model is regularized by appropriate priors on the unitary transformations, posterior summaries of which may then be suitably interpreted as optimal data-driven rotations of a fixed orthonormal basis for the Hilbert space. Our numerical experiments demonstrate utility of the proposed model, and superiority over the current state-of-the-art.

Generative Models · Diffusion models

François Rozet, Gerome Andry, Francois Lanusse, Gilles Louppe

Diffusion models recently proved to be remarkable priors for Bayesian inverse problems. However, training these models typically requires access to large amounts of clean data, which could prove difficult in some settings. In this work, we present a novel method based on the expectation-maximization algorithm for training diffusion models from incomplete and noisy observations only. Unlike previous works, our method leads to proper diffusion models, which is crucial for downstream tasks. As part of our method, we propose and motivate an improved posterior sampling scheme for unconditional diffusion models. We present empirical evidence supporting the effectiveness of our method.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Jake Snell, Gianluca Bencomo, Tom Griffiths

Most applications of machine learning to classification assume a closed set of balanced classes. This is at odds with the real world, where class occurrence statistics often follow a long-tailed power-law distribution and it is unlikely that all classes are seen in a single sample. Nonparametric Bayesian models naturally capture this phenomenon, but have significant practical barriers to widespread adoption, namely implementation complexity and computational inefficiency. To address this, we present a method for extracting the inductive bias from a nonparametric Bayesian model and transferring it to an artificial neural network. By simulating data with a nonparametric Bayesian prior, we can metalearn a sequence model that performs inference over an unlimited set of classes. After training, this "neural circuit" has distilled the corresponding inductive bias and can successfully perform sequential inference over an open set of classes. Our experimental results show that the metalearned neural circuit achieves comparable or better performance than particle filter-based methods for inference in these models while being faster and simpler to use than methods that explicitly incorporate Bayesian nonparametric inference.

Probabilistic Methods · Gaussian Processes

Sebastian Ament, Elizabeth Santorella, David Eriksson, Ben Letham, Maximilian Balandat, Eytan Bakshy

Gaussian processes (GPs) are non-parametric probabilistic regression models that are popular due to their flexibility, data efficiency, and well-calibrated uncertainty estimates. However, standard GP models assume homoskedastic Gaussian noise, while many real-world applications are subject to non-Gaussian corruptions. Variants of GPs that are more robust to alternative noise models have been proposed, and entail significant trade-offs between accuracy and robustness, and between computational requirements and theoretical guarantees. In this work, we propose and study a GP model that achieves robustness against sparse outliers by inferring data-point-specific noise levels with a sequential selection procedure maximizing the log marginal likelihood that we refer to as relevance pursuit. We show, surprisingly, that the model can be parameterized such that the associated log marginal likelihood is strongly concave in the data-point-specific noise variances, a property rarely found in either robust regression objectives or GP marginal likelihoods. This in turn implies the weak submodularity of the corresponding subset selection problem, and thereby proves approximation guarantees for the proposed algorithm. We compare the model’s performance relative to other approaches on diverse regression and Bayesian optimization tasks, including the challenging but common setting of sparse corruptions of the labels within or close to the function range.

Probabilistic Methods · Bayesian Models and Methods

Rafael Oliveira, Dino Sejdinovic, David Howard, Edwin Bonilla

The process of calibrating computer models of natural phenomena is essential for applications in the physical sciences, where plenty of domain knowledge can be embedded into simulations and then calibrated against real observations. Current machine learning approaches, however, mostly rely on rerunning simulations over a fixed set of designs available in the observed data, potentially neglecting informative correlations across the design space and requiring a large amount of simulations. Instead, we consider the calibration process from the perspective of Bayesian adaptive experimental design and propose a data-efficient algorithm to run maximally informative simulations within a batch-sequential process. At each round, the algorithm jointly estimates the parameters posterior distribution and optimal designs by maximising a variational lower bound of the expected information gain. The simulator is modelled as a sample from a Gaussian process, which allows us to correlate simulations and real data with the unknown calibration parameters. We show the benefits of our method when compared to related approaches across synthetic and real-data problems.

Probabilistic Methods · Bayesian Models and Methods

Amber Hu, David Zoltowski, Aditya Nair, David Anderson, Lea Duncker, Scott Linderman

Understanding how the collective activity of neural populations relates to computation and ultimately behavior is a key goal in neuroscience. To this end, statistical methods which describe high-dimensional neural time series in terms of low-dimensional latent dynamics have played a fundamental role in characterizing neural systems. Yet, what constitutes a successful method involves two opposing criteria: (1) methods should be expressive enough to capture complex nonlinear dynamics, and (2) they should maintain a notion of interpretability often only warranted by simpler linear models. In this paper, we develop an approach that balances these two objectives: the Gaussian Process Switching Linear Dynamical System (gpSLDS). Our method builds on previous work modeling the latent state evolution via a stochastic differential equation whose nonlinear dynamics are described by a Gaussian process (GP-SDEs). We propose a novel kernel function which enforces smoothly interpolated locally linear dynamics, and therefore expresses flexible -- yet interpretable -- dynamics akin to those of recurrent switching linear dynamical systems (rSLDS). Our approach resolves key limitations of the rSLDS such as artifactual oscillations in dynamics near discrete state boundaries, while also providing posterior uncertainty estimates of the dynamics. To fit our models, we leverage a modified learning objective which improves the estimation accuracy of kernel hyperparameters compared to previous GP-SDE fitting approaches. We apply our method to synthetic data and data recorded in two neuroscience experiments and demonstrate favorable performance in comparison to the rSLDS.

Probabilistic Methods · Bayesian Models and Methods

Sam Griesemer, Defu Cao, Zijun Cui, Carolina Osorio, Yan Liu

Computer simulations have long presented the exciting possibility of scientific insight into complex real-world processes. Despite the power of modern computing, however, it remains challenging to systematically perform inference under simulation models. This has led to the rise of simulation-based inference (SBI), a class of machine learning-enabled techniques for approaching inverse problems with stochastic simulators. Many such methods, however, require large numbers of simulation samples and face difficulty scaling to high-dimensional settings, often making inference prohibitive under resource-intensive simulators. To mitigate these drawbacks, we introduce active sequential neural posterior estimation (ASNPE). ASNPE brings an active learning scheme into the inference loop to estimate the utility of simulation parameter candidates to the underlying probabilistic model. The proposed acquisition scheme is easily integrated into existing posterior estimation pipelines, allowing for improved sample efficiency with low computational overhead. We further demonstrate the effectiveness of the proposed method in the travel demand calibration setting, a high-dimensional inverse problem commonly requiring computationally expensive traffic simulators. Our method outperforms well-tuned benchmarks and state-of-the-art posterior estimation methods on a large-scale real-world traffic network, as well as demonstrates a performance advantage over non-active counterparts on a suite of SBI benchmark environments.

Probabilistic Methods · Bayesian Models and Methods

Tristan Cinquin, Marvin Pförtner, Vincent Fortuin, Philipp Hennig, Robert Bamler

Laplace approximations are popular techniques for endowing deep networks with epistemic uncertainty estimates as they can be applied without altering the predictions of the trained network, and they scale to large models and datasets. While the choice of prior strongly affects the resulting posterior distribution, computational tractability and lack of interpretability of the weight space typically limit the Laplace approximation to isotropic Gaussian priors, which are known to cause pathological behavior as depth increases. As a remedy, we directly place a prior on function space. More precisely, since Lebesgue densities do not exist on infinite-dimensional function spaces, we recast training as finding the so-called weak mode of the posterior measure under a Gaussian process (GP) prior restricted to the space of functions representable by the neural network. Through the GP prior, one can express structured and interpretable inductive biases, such as regularity or periodicity, directly in function space, while still exploiting the implicit inductive biases that allow deep networks to generalize. After model linearization, the training objective induces a negative log-posterior density to which we apply a Laplace approximation, leveraging highly scalable methods from matrix-free linear algebra. Our method provides improved results where prior knowledge is abundant (as is the case in many scientific inference tasks). At the same time, it stays competitive for black-box supervised learning problems, where neural networks typically excel.

Language

Yi Ren, Shangmin Guo, Linlu Qiu, Bailin Wang, Danica J. Sutherland

With the widespread adoption of Large Language Models (LLMs), the prevalence of iterative interactions among these models is anticipated to increase. Notably, recent advancements in multi-round on-policy self-improving methods allow LLMs to generate new examples for training subsequent models. At the same time, multi-agent LLM systems, involving automated interactions among agents, are also increasing in prominence. Thus, in both short and long terms, LLMs may actively engage in an evolutionary process. We draw parallels between the behavior of LLMs and the evolution of human culture, as the latter has been extensively studied by cognitive scientists for decades. Our approach involves leveraging Iterated Learning (IL), a Bayesian framework that elucidates how subtle biases are magnified during human cultural evolution, to explain some behaviors of LLMs. This paper outlines key characteristics of agents' behavior in the Bayesian-IL framework, including predictions that are supported by experimental verification with various LLMs. This theoretical framework could help to more effectively predict and guide the evolution of LLMs in desired directions.

Computational Biology

Jiayu Qin, Jian Chen, Rohan Sharma, Jingchen Sun, Changyou Chen

Contrastive Learning (CL) plays a crucial role in molecular representation learning, enabling unsupervised learning from large scale unlabeled molecule datasets. It has inspired various applications in molecular property prediction and drug design.However, existing molecular representation learning methods often introduce potential false positive and false negative pairs through conventional graph augmentations like node masking and subgraph removal. The issue can lead to suboptimal performance when applying standard contrastive learning techniques to molecular datasets. To address the issue of false positive and negative pairs in molecular representation learning, we propose a novel probability-based contrastive learning (CL) framework. Unlike conventional methods, our approach introduces a learnable weight distribution via Bayesian modeling to automatically identify and mitigate false positive and negative pairs. This method is particularly effective because it dynamically adjusts to the data, improving the accuracy of the learned representations. Our model is learned by a stochastic expectation-maximization process, which optimizes the model by iteratively refining the probability estimates of sample weights and updating the model parameters.Experimental results indicate that our method outperforms existing approaches in 13 out of 15 molecular property prediction benchmarks in MoleculeNet dataset and 8 out of 12 benchmarks in the QM9 benchmark, achieving new state-of-the-art results on average.